How do I use the quotient property to explain the definition of negative exponents

Question

I'm confused

Answer 1

-Negative exponent definition

x^-1=1/x

1/(x^-1)=x

---------

x^-a=1/(x^a)

 

-Quotient property

(x/y)²=(x²)/(y²)

sqrt(x/y)=sqrt(x)/sqrt(y)

--------

(x/y)^a=(x^a) / (y^a)

 

-Power Rules

x^a*x^b=x^(a+b)

(x^a)b=x^(a*b)

 

-So

(x⁶)/(x⁸)=x^(6-8)=x^-2

and

x⁰=1

1/x=x⁰/x¹=x^(0-1)=x^-1

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Which is just the negative exponent rule where

1/x=x^-1